Problem: Simplify the expression. $(5r-5)(3r+7)$
First distribute the ${5r-5}$ onto the ${3r}$ and ${7}$ $ = {3r}({5r-5}) + {7}({5r-5})$ Then distribute the ${3r}.$ $ = ({3r} \times {5r}) + ({3r} \times {-5}) + {7}({5r-5})$ $ = 15r^{2} - 15r + {7}({5r-5})$ Then distribute the ${7}$ $ = 15r^{2} - 15r + ({7} \times {5r}) + ({7} \times {-5})$ $ = 15r^{2} - 15r + 35r - 35$ Finally, combine the $x$ terms. $ = 15r^{2} + 20r - 35$